[lmilcin]

It is not about how often they come up but whether you can think in an abstract way on a convoluted problem.

Think about IQ test which shows some abstract puzzles that have no connection with the real world. They are part of the test because they provide measurement points on tasks that require different types of abstract thinking without prerequisite knowledge.

Again, it is not possible to verify you have all the necessary knowledge for the job, nor would it be useful (no candidate knows everything for the position and if he did he would likely be overqualified).

I of course ask questions that test candidate's knowledge in the most useful areas, but at least part of the interview I want to devote to finding out how smart he/she is on abstract tasks that don't require some special knowledge.

[sukilot]

I don't want to let abstract convoluted problem solvers anywhere near my production systems

[mlyle]

You probably want to avoid people with a propensity for viewing things in abstract and convoluted terms... not to avoid people with the ability to solve abstract and/or convoluted problems.